If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 64 cars is selected,there is approximately a 95.44% chance that the sample mean will be between 14 and 16 gallons.

Question

Quizplus · Accepted Answer

This is a statement about a confidence interval for the sample mean. Given a sample size of 64, the standard error of the mean is:

SE = σ/√n = 4/√64 = 0.5

To calculate the 95% confidence interval for the sample mean, we can use the formula:

CI = x̄ ± z*SE

where x̄ is the sample mean, z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for 95%), and SE is the standard error of the mean.

Substituting in the values given in the problem, we get:

CI = 15 ± 1.96*0.5
CI = (14, 16)

This means that we are 95% confident that the true population mean lies between 14 and 16 gallons. Therefore, the statement in the question is true.

If the Amount of Gasoline Purchased Per Car at a Large